Percent Applications

Percentages are everywhere in daily life. This page covers the most common real-world applications: sales tax, tips, discounts, markups, simple interest, and commission. Each follows the same core skill — finding a percent of a number — applied in a specific context.

Sales Tax

Sales tax is a percentage added to the price of a purchase. The tax rate varies by location.

Formula:

$\text{Tax Amount} = \text{Price} \times \text{Tax Rate}$

$\text{Total Cost} = \text{Price} + \text{Tax Amount}$

Or in one step:

$\text{Total Cost} = \text{Price} \times (1 + \text{Tax Rate})$

Example 1: Calculate Sales Tax

You buy a laptop for $850 and the sales tax rate is 8.5%.

$\text{Tax} = 850 \times 0.085 = 72.25$

$\text{Total} = 850 + 72.25 = 922.25$

Answer: $922.25

Tips

A tip (or gratuity) is a percentage of the bill, typically given for service.

Common Tip Percentages

Example 2: Calculate a Tip

Your restaurant bill is $64. You want to leave a 20% tip.

$\text{Tip} = 64 \times 0.20 = 12.80$

$\text{Total} = 64 + 12.80 = 76.80$

Answer: $12.80 tip, $76.80 total

Quick Tip Trick: The 10% Method

To estimate a tip mentally:

• Find 10% (move the decimal left one place)
• Double it for 20%, or add half of it for 15%

For a $64 bill: 10% = $6.40, so 20% = $12.80 and 15% = $6.40 + $3.20 = $9.60.

Discounts

A discount is a percentage taken off the original price.

Formulas:

$\text{Discount Amount} = \text{Original Price} \times \text{Discount Rate}$

$\text{Sale Price} = \text{Original Price} - \text{Discount Amount}$

Or in one step:

$\text{Sale Price} = \text{Original Price} \times (1 - \text{Discount Rate})$

Example 3: Calculate a Discount

A $120 jacket is 30% off.

$\text{Sale Price} = 120 \times (1 - 0.30) = 120 \times 0.70 = 84$

Answer: $84

Example 4: Discount Plus Tax

That same $120 jacket is 30% off with 7% sales tax. What do you actually pay?

Step 1: Find the sale price: $120 \times 0.70 = 84$

Step 2: Apply tax to the sale price: $84 \times 1.07 = 89.88$

Answer: $89.88

Note: Tax is calculated on the discounted price, not the original price.

Markups

A markup is the percentage a seller adds to the cost of a product to set the selling price. It is the opposite of a discount — the seller increases the price.

Formula:

$\text{Selling Price} = \text{Cost} \times (1 + \text{Markup Rate})$

Example 5: Calculate a Markup

A store buys a shirt for $18 and applies a 60% markup.

$\text{Selling Price} = 18 \times (1 + 0.60) = 18 \times 1.60 = 28.80$

Answer: $28.80

Simple Interest

Simple interest is calculated only on the original amount (the principal). It is used for short-term loans, savings accounts, and some bonds.

Formula:

$I = P \times r \times t$

Where:

• $I$ = interest earned (or owed)
• $P$ = principal (starting amount)
• $r$ = annual interest rate (as a decimal)
• $t$ = time in years

$\text{Total Amount} = P + I = P(1 + rt)$

Example 6: Savings Account

You deposit $2,000 in an account earning 4% simple interest per year. How much interest do you earn in 3 years?

$I = 2{,}000 \times 0.04 \times 3 = 240$

$\text{Total} = 2{,}000 + 240 = 2{,}240$

Answer: $240 in interest, $2,240 total

Example 7: Short-Term Loan

You borrow $5,000 at 6% simple interest for 18 months (1.5 years).

$I = 5{,}000 \times 0.06 \times 1.5 = 450$

Answer: You owe $450 in interest

Commission

A commission is a percentage of sales that a salesperson earns as income.

Formula:

$\text{Commission} = \text{Total Sales} \times \text{Commission Rate}$

Example 8: Sales Commission

A real estate agent earns a 3% commission. They sell a house for $350,000.

$\text{Commission} = 350{,}000 \times 0.03 = 10{,}500$

Answer: $10,500

Example 9: Base Salary Plus Commission

A salesperson earns $2,000 per month base salary plus 5% commission on sales. Last month, they sold $18,000 worth of products.

$\text{Commission} = 18{,}000 \times 0.05 = 900$

$\text{Total Earnings} = 2{,}000 + 900 = 2{,}900$

Answer: $2,900

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Sales tax: price × (1 + rate) = total
• Tips: bill × tip rate = tip amount
• Discounts: price × (1 − discount rate) = sale price
• Tax on discounted items: apply discount first, then tax
• Simple interest: $I = P \times r \times t$
• Commission: total sales × commission rate
• All of these are applications of the same skill: finding a percent of a number

Return to Arithmetic for more foundational math topics.